Codeforces Round 449 (Div. 1) |
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Finished |

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data structures

probabilities

*2600

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C. Willem, Chtholly and Seniorious

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard output— Willem...

— What's the matter?

— It seems that there's something wrong with Seniorious...

— I'll have a look...

Seniorious is made by linking special talismans in particular order.

After over 500 years, the carillon is now in bad condition, so Willem decides to examine it thoroughly.

Seniorious has *n* pieces of talisman. Willem puts them in a line, the *i*-th of which is an integer *a*_{i}.

In order to maintain it, Willem needs to perform *m* operations.

There are four types of operations:

- 1
*l**r**x*: For each*i*such that*l*≤*i*≤*r*, assign*a*_{i}+*x*to*a*_{i}. - 2
*l**r**x*: For each*i*such that*l*≤*i*≤*r*, assign*x*to*a*_{i}. - 3
*l**r**x*: Print the*x*-th smallest number in the index range [*l*,*r*], i.e. the element at the*x*-th position if all the elements*a*_{i}such that*l*≤*i*≤*r*are taken and sorted into an array of non-decreasing integers. It's guaranteed that 1 ≤*x*≤*r*-*l*+ 1. - 4
*l**r**x**y*: Print the sum of the*x*-th power of*a*_{i}such that*l*≤*i*≤*r*, modulo*y*, i.e. .

Input

The only line contains four integers *n*, *m*, *seed*, *v*_{max} (1 ≤ *n*, *m* ≤ 10^{5}, 0 ≤ *seed* < 10^{9} + 7, 1 ≤ *vmax* ≤ 10^{9}).

The initial values and operations are generated using following pseudo code:

def rnd():

ret = seed

seed = (seed * 7 + 13) mod 1000000007

return ret

for i = 1 to n:

a[i] = (rnd() mod vmax) + 1

for i = 1 to m:

op = (rnd() mod 4) + 1

l = (rnd() mod n) + 1

r = (rnd() mod n) + 1

if (l > r):

swap(l, r)

if (op == 3):

x = (rnd() mod (r - l + 1)) + 1

else:

x = (rnd() mod vmax) + 1

if (op == 4):

y = (rnd() mod vmax) + 1

Here *op* is the type of the operation mentioned in the legend.

Output

For each operation of types 3 or 4, output a line containing the answer.

Examples

Input

10 10 7 9

Output

2

1

0

3

Input

10 10 9 9

Output

1

1

3

3

Note

In the first example, the initial array is {8, 9, 7, 2, 3, 1, 5, 6, 4, 8}.

The operations are:

- 2 6 7 9
- 1 3 10 8
- 4 4 6 2 4
- 1 4 5 8
- 2 1 7 1
- 4 7 9 4 4
- 1 2 7 9
- 4 5 8 1 1
- 2 5 7 5
- 4 3 10 8 5

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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